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B Kinematic equation without time

  1. Sep 28, 2016 #1
    I understand most of the kinematic equations, but there is just this one equation that omits time from the equation. I always end up with V02+2a(x - x0) = 2V0V + V2

    The 2V0V part is what I don't understand how to get rid of. So if you please could you do the equation with steps , I would be very grateful. Thank you.
     
  2. jcsd
  3. Sep 28, 2016 #2

    Ibix

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    What are the steps you took to get to that equation?
     
  4. Sep 28, 2016 #3
    t = (V - V0)/a

    x - x0 = V0((V-V0)/a) + .5a((V - V0/a)2)

    x - x0 = (V0V - V02)/a + (V2 + V02)/2a

    2a(x - x0) = 2V0V -2V02 + V2 +V02

    V02+2a(x - x0) = 2V0V + V2
     
  5. Sep 28, 2016 #4

    Ibix

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    What do you get if you expand ##(V-V_0)^2##?

    Edit: By the way, something seems to be wrong with the brackets in the last term of your second equation. I assumed that was just a typo, but if they look right to you then you need tk think about that too.
     
    Last edited: Sep 28, 2016
  6. Sep 28, 2016 #5
    Oh I see what I did wrong. As you intimated, I did not expand (V - V0)2 correctly. Now I have -2V0V to cancel out.
     
  7. Sep 29, 2016 #6

    Ibix

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    That's right. Algebraic slips can be hard to spot. I sometimes write each term on a separate line when I'm expanding brackets, which makes it easier for me to not get distracted when I'm doing it. Then when I'm collecting terms together I put a little tick above each one as I copy it on to the next line so I don't lose one or double one up by accident. You can also count terms. You know that ##(V-V_0)^2## should give you three terms when expanded - that would have caught this error because your expansion only had two.
     
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